Bryson, Vershynin, and Zhao [1]} show that the limiting spectral distribution of \(\widehat{\Sigma }_N\)  is the Marchenko-Pastur (MP) law if \(N\rightarrow \infty \) , \(\binom{n}{d}/N\)  tends to a positive constant, the fourth moments of \(X_\alpha =X_{\alpha }(d,n)\)  are uniformly bounded, and \(d^3=o(n).\)  However, they conjecture that the optimal condition is \(d^2=o(n)\) . We prove this conjecture in our paper. The proof is based on a general version of the MP theorem and a new concentration inequality for quadratic forms in symmetric random tensors.
